Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8640,2,Mod(1,8640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8640 = 2^{6} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8640.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(68.9907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 135) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8640.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60555 | −0.984806 | −0.492403 | − | 0.870367i | \(-0.663881\pi\) | ||||
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.60555 | 1.38863 | 0.694313 | − | 0.719673i | \(-0.255708\pi\) | ||||
0.694313 | + | 0.719673i | \(0.255708\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.60555 | −1.83205 | −0.916025 | − | 0.401121i | \(-0.868621\pi\) | ||||
−0.916025 | + | 0.401121i | \(0.868621\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.60555 | −0.389403 | −0.194702 | − | 0.980863i | \(-0.562374\pi\) | ||||
−0.194702 | + | 0.980863i | \(0.562374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.60555 | −0.827170 | −0.413585 | − | 0.910465i | \(-0.635724\pi\) | ||||
−0.413585 | + | 0.910465i | \(0.635724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | 0.625543 | 0.312772 | − | 0.949828i | \(-0.398743\pi\) | ||||
0.312772 | + | 0.949828i | \(0.398743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.39445 | 0.258943 | 0.129471 | − | 0.991583i | \(-0.458672\pi\) | ||||
0.129471 | + | 0.991583i | \(0.458672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.60555 | −1.00679 | −0.503393 | − | 0.864057i | \(-0.667915\pi\) | ||||
−0.503393 | + | 0.864057i | \(0.667915\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.60555 | −0.440419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.60555 | 0.719266 | 0.359633 | − | 0.933094i | \(-0.382902\pi\) | ||||
0.359633 | + | 0.933094i | \(0.382902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.605551 | −0.0923457 | −0.0461729 | − | 0.998933i | \(-0.514703\pi\) | ||||
−0.0461729 | + | 0.998933i | \(0.514703\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.21110 | 1.34358 | 0.671789 | − | 0.740743i | \(-0.265526\pi\) | ||||
0.671789 | + | 0.740743i | \(0.265526\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.211103 | −0.0301575 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.60555 | 0.220539 | 0.110270 | − | 0.993902i | \(-0.464829\pi\) | ||||
0.110270 | + | 0.993902i | \(0.464829\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.60555 | 0.621012 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.39445 | −0.181542 | −0.0907709 | − | 0.995872i | \(-0.528933\pi\) | ||||
−0.0907709 | + | 0.995872i | \(0.528933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.21110 | 0.539176 | 0.269588 | − | 0.962976i | \(-0.413112\pi\) | ||||
0.269588 | + | 0.962976i | \(0.413112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.60555 | −0.819318 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.788897 | 0.0963792 | 0.0481896 | − | 0.998838i | \(-0.484655\pi\) | ||||
0.0481896 | + | 0.998838i | \(0.484655\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.39445 | −0.877560 | −0.438780 | − | 0.898595i | \(-0.644589\pi\) | ||||
−0.438780 | + | 0.898595i | \(0.644589\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6056 | 1.47537 | 0.737684 | − | 0.675146i | \(-0.235919\pi\) | ||||
0.737684 | + | 0.675146i | \(0.235919\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | −1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6056 | −1.30573 | −0.652863 | − | 0.757476i | \(-0.726432\pi\) | ||||
−0.652863 | + | 0.757476i | \(0.726432\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.00000 | 0.329293 | 0.164646 | − | 0.986353i | \(-0.447352\pi\) | ||||
0.164646 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.60555 | −0.174146 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.8167 | 1.46456 | 0.732281 | − | 0.681002i | \(-0.238456\pi\) | ||||
0.732281 | + | 0.681002i | \(0.238456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.2111 | 1.80421 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.60555 | −0.369922 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.2111 | 1.43094 | 0.715470 | − | 0.698643i | \(-0.246213\pi\) | ||||
0.715470 | + | 0.698643i | \(0.246213\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00000 | 0.279751 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.18335 | 0.383487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2111 | 0.928282 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.2111 | −1.70471 | −0.852355 | − | 0.522964i | \(-0.824826\pi\) | ||||
−0.852355 | + | 0.522964i | \(0.824826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.39445 | 0.814602 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.8167 | −1.43674 | −0.718372 | − | 0.695659i | \(-0.755112\pi\) | ||||
−0.718372 | + | 0.695659i | \(0.755112\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −30.4222 | −2.54403 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.39445 | 0.115803 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.0278 | 1.88651 | 0.943254 | − | 0.332073i | \(-0.107748\pi\) | ||||
0.943254 | + | 0.332073i | \(0.107748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.4222 | 1.17366 | 0.586831 | − | 0.809709i | \(-0.300375\pi\) | ||||
0.586831 | + | 0.809709i | \(0.300375\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.60555 | −0.450249 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.8167 | 1.42192 | 0.710962 | − | 0.703231i | \(-0.248260\pi\) | ||||
0.710962 | + | 0.703231i | \(0.248260\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.81665 | −0.616039 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | −0.156652 | −0.0783260 | − | 0.996928i | \(-0.524958\pi\) | ||||
−0.0783260 | + | 0.996928i | \(0.524958\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00000 | 0.232147 | 0.116073 | − | 0.993241i | \(-0.462969\pi\) | ||||
0.116073 | + | 0.993241i | \(0.462969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.6333 | 2.35641 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.8167 | −0.822375 | −0.411187 | − | 0.911551i | \(-0.634886\pi\) | ||||
−0.411187 | + | 0.911551i | \(0.634886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.60555 | −0.196961 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.2111 | −1.58539 | −0.792696 | − | 0.609617i | \(-0.791323\pi\) | ||||
−0.792696 | + | 0.609617i | \(0.791323\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | −0.147043 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.39445 | −0.540736 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.4222 | 0.898839 | 0.449420 | − | 0.893321i | \(-0.351631\pi\) | ||||
0.449420 | + | 0.893321i | \(0.351631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.183346 | 0.0131975 | 0.00659877 | − | 0.999978i | \(-0.497900\pi\) | ||||
0.00659877 | + | 0.999978i | \(0.497900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.8167 | −1.62562 | −0.812810 | − | 0.582529i | \(-0.802063\pi\) | ||||
−0.812810 | + | 0.582529i | \(0.802063\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.21110 | −0.0858528 | −0.0429264 | − | 0.999078i | \(-0.513668\pi\) | ||||
−0.0429264 | + | 0.999078i | \(0.513668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.63331 | −0.255008 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.60555 | 0.321666 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.6056 | −1.14863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.81665 | 0.606963 | 0.303482 | − | 0.952837i | \(-0.401851\pi\) | ||||
0.303482 | + | 0.952837i | \(0.401851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.605551 | −0.0412983 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.6056 | 0.991489 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.6056 | 0.713407 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0000 | −0.669650 | −0.334825 | − | 0.942280i | \(-0.608677\pi\) | ||||
−0.334825 | + | 0.942280i | \(0.608677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.7889 | −0.782457 | −0.391228 | − | 0.920294i | \(-0.627950\pi\) | ||||
−0.391228 | + | 0.920294i | \(0.627950\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.21110 | −0.542605 | −0.271302 | − | 0.962494i | \(-0.587454\pi\) | ||||
−0.271302 | + | 0.962494i | \(0.587454\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.21110 | 0.600866 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2111 | 0.983924 | 0.491962 | − | 0.870617i | \(-0.336280\pi\) | ||||
0.491962 | + | 0.870617i | \(0.336280\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7889 | 0.888221 | 0.444110 | − | 0.895972i | \(-0.353520\pi\) | ||||
0.444110 | + | 0.895972i | \(0.353520\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.211103 | −0.0134868 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.8167 | 1.51542 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.6333 | 1.74420 | 0.872099 | − | 0.489329i | \(-0.162758\pi\) | ||||
0.872099 | + | 0.489329i | \(0.162758\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.8167 | 0.868646 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.18335 | −0.0738151 | −0.0369076 | − | 0.999319i | \(-0.511751\pi\) | ||||
−0.0369076 | + | 0.999319i | \(0.511751\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.21110 | 0.323802 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.78890 | 0.171971 | 0.0859854 | − | 0.996296i | \(-0.472596\pi\) | ||||
0.0859854 | + | 0.996296i | \(0.472596\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.60555 | 0.0986282 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.21110 | −0.195784 | −0.0978922 | − | 0.995197i | \(-0.531210\pi\) | ||||
−0.0978922 | + | 0.995197i | \(0.531210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.2389 | 1.89763 | 0.948813 | − | 0.315839i | \(-0.102286\pi\) | ||||
0.948813 | + | 0.315839i | \(0.102286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.60555 | 0.277725 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.02776 | −0.422257 | −0.211128 | − | 0.977458i | \(-0.567714\pi\) | ||||
−0.211128 | + | 0.977458i | \(0.567714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.8167 | 1.18216 | 0.591081 | − | 0.806612i | \(-0.298701\pi\) | ||||
0.591081 | + | 0.806612i | \(0.298701\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.39445 | −0.201779 | −0.100890 | − | 0.994898i | \(-0.532169\pi\) | ||||
−0.100890 | + | 0.994898i | \(0.532169\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.4222 | −0.848365 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.18335 | −0.419656 | −0.209828 | − | 0.977738i | \(-0.567290\pi\) | ||||
−0.209828 | + | 0.977738i | \(0.567290\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.39445 | −0.0811879 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.8167 | −1.14603 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.57779 | 0.0909426 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.21110 | 0.241127 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.42221 | −0.480681 | −0.240340 | − | 0.970689i | \(-0.577259\pi\) | ||||
−0.240340 | + | 0.970689i | \(0.577259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.81665 | 0.443242 | 0.221621 | − | 0.975133i | \(-0.428865\pi\) | ||||
0.221621 | + | 0.975133i | \(0.428865\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.6333 | −1.10974 | −0.554870 | − | 0.831937i | \(-0.687232\pi\) | ||||
−0.554870 | + | 0.831937i | \(0.687232\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.60555 | −0.427170 | −0.213585 | − | 0.976924i | \(-0.568514\pi\) | ||||
−0.213585 | + | 0.976924i | \(0.568514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.42221 | 0.359574 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.78890 | 0.322103 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.60555 | −0.366410 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.2111 | −1.60559 | −0.802794 | − | 0.596257i | \(-0.796654\pi\) | ||||
−0.802794 | + | 0.596257i | \(0.796654\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.788897 | 0.0431021 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.60555 | 0.359827 | 0.179914 | − | 0.983682i | \(-0.442418\pi\) | ||||
0.179914 | + | 0.983682i | \(0.442418\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.8167 | −1.39805 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.7889 | 1.01451 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.4222 | 1.63315 | 0.816575 | − | 0.577240i | \(-0.195870\pi\) | ||||
0.816575 | + | 0.577240i | \(0.195870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.8444 | 1.70459 | 0.852296 | − | 0.523060i | \(-0.175209\pi\) | ||||
0.852296 | + | 0.523060i | \(0.175209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.6333 | −1.15142 | −0.575712 | − | 0.817652i | \(-0.695275\pi\) | ||||
−0.575712 | + | 0.817652i | \(0.695275\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.39445 | −0.392457 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.63331 | 0.508427 | 0.254213 | − | 0.967148i | \(-0.418183\pi\) | ||||
0.254213 | + | 0.967148i | \(0.418183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.00000 | −0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.6056 | 0.659805 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.60555 | −0.136009 | −0.0680043 | − | 0.997685i | \(-0.521663\pi\) | ||||
−0.0680043 | + | 0.997685i | \(0.521663\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.18335 | −0.217189 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.2111 | 1.30538 | 0.652691 | − | 0.757624i | \(-0.273640\pi\) | ||||
0.652691 | + | 0.757624i | \(0.273640\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.21110 | −0.474396 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6056 | −1.10980 | −0.554901 | − | 0.831916i | \(-0.687244\pi\) | ||||
−0.554901 | + | 0.831916i | \(0.687244\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.6333 | −1.25870 | −0.629352 | − | 0.777121i | \(-0.716679\pi\) | ||||
−0.629352 | + | 0.777121i | \(0.716679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | −0.611577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.8167 | 1.30896 | 0.654478 | − | 0.756081i | \(-0.272888\pi\) | ||||
0.654478 | + | 0.756081i | \(0.272888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.81665 | −0.243589 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.6056 | −0.583939 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.39445 | 0.270740 | 0.135370 | − | 0.990795i | \(-0.456778\pi\) | ||||
0.135370 | + | 0.990795i | \(0.456778\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.0278 | 1.84448 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.21110 | −0.456577 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | 0.247234 | 0.123617 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123617 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.63331 | 0.178783 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.00000 | 0.147264 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.0278 | 1.12498 | 0.562490 | − | 0.826804i | \(-0.309844\pi\) | ||||
0.562490 | + | 0.826804i | \(0.309844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.42221 | −0.264262 | −0.132131 | − | 0.991232i | \(-0.542182\pi\) | ||||
−0.132131 | + | 0.991232i | \(0.542182\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.60555 | −0.0778807 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.9722 | −0.530984 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.18335 | −0.201505 | −0.100752 | − | 0.994912i | \(-0.532125\pi\) | ||||
−0.100752 | + | 0.994912i | \(0.532125\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.2389 | 1.06873 | 0.534366 | − | 0.845253i | \(-0.320551\pi\) | ||||
0.534366 | + | 0.845253i | \(0.320551\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.8167 | −0.517431 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.6056 | 1.31754 | 0.658771 | − | 0.752344i | \(-0.271077\pi\) | ||||
0.658771 | + | 0.752344i | \(0.271077\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.6333 | −1.17036 | −0.585182 | − | 0.810902i | \(-0.698977\pi\) | ||||
−0.585182 | + | 0.810902i | \(0.698977\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.8167 | 0.654972 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.2389 | −1.80460 | −0.902302 | − | 0.431105i | \(-0.858124\pi\) | ||||
−0.902302 | + | 0.431105i | \(0.858124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.2111 | 0.998792 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.2111 | 0.806869 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.2111 | −0.617989 | −0.308995 | − | 0.951064i | \(-0.599993\pi\) | ||||
−0.308995 | + | 0.951064i | \(0.599993\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.6333 | 1.00756 | 0.503782 | − | 0.863831i | \(-0.331942\pi\) | ||||
0.503782 | + | 0.863831i | \(0.331942\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.788897 | −0.0366632 | −0.0183316 | − | 0.999832i | \(-0.505835\pi\) | ||||
−0.0183316 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2111 | 0.565062 | 0.282531 | − | 0.959258i | \(-0.408826\pi\) | ||||
0.282531 | + | 0.959258i | \(0.408826\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.05551 | −0.0949148 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.78890 | −0.128234 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.60555 | −0.165434 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.8167 | 1.72789 | 0.863944 | − | 0.503589i | \(-0.167987\pi\) | ||||
0.863944 | + | 0.503589i | \(0.167987\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.2111 | 0.602374 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.00000 | 0.363261 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.8167 | −1.35112 | −0.675561 | − | 0.737304i | \(-0.736098\pi\) | ||||
−0.675561 | + | 0.737304i | \(0.736098\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.2111 | 1.22802 | 0.614010 | − | 0.789298i | \(-0.289555\pi\) | ||||
0.614010 | + | 0.789298i | \(0.289555\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.23886 | −0.100833 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.2666 | 0.864226 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.3944 | 0.912981 | 0.456490 | − | 0.889728i | \(-0.349106\pi\) | ||||
0.456490 | + | 0.889728i | \(0.349106\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.57779 | −0.114938 | −0.0574691 | − | 0.998347i | \(-0.518303\pi\) | ||||
−0.0574691 | + | 0.998347i | \(0.518303\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.8444 | −1.10121 | −0.550605 | − | 0.834766i | \(-0.685603\pi\) | ||||
−0.550605 | + | 0.834766i | \(0.685603\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.8444 | −1.45295 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.00000 | −0.176261 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 42.4222 | 1.86573 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.6056 | 1.25323 | 0.626616 | − | 0.779328i | \(-0.284439\pi\) | ||||
0.626616 | + | 0.779328i | \(0.284439\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6056 | −1.33829 | −0.669144 | − | 0.743133i | \(-0.733339\pi\) | ||||
−0.669144 | + | 0.743133i | \(0.733339\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.00000 | 0.392046 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.4222 | −1.31773 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.972244 | −0.0418775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.4222 | 1.73789 | 0.868943 | − | 0.494912i | \(-0.164800\pi\) | ||||
0.868943 | + | 0.494912i | \(0.164800\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.00000 | 0.299847 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.605551 | −0.0258915 | −0.0129458 | − | 0.999916i | \(-0.504121\pi\) | ||||
−0.0129458 | + | 0.999916i | \(0.504121\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.02776 | −0.214190 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.2389 | 1.28589 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.63331 | 0.408176 | 0.204088 | − | 0.978953i | \(-0.434577\pi\) | ||||
0.204088 | + | 0.978953i | \(0.434577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.0000 | 1.01148 | 0.505740 | − | 0.862686i | \(-0.331220\pi\) | ||||
0.505740 | + | 0.862686i | \(0.331220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.2111 | 0.639936 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.1833 | −0.678441 | −0.339221 | − | 0.940707i | \(-0.610163\pi\) | ||||
−0.339221 | + | 0.940707i | \(0.610163\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4500 | −1.19059 | −0.595297 | − | 0.803506i | \(-0.702966\pi\) | ||||
−0.595297 | + | 0.803506i | \(0.702966\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.00000 | 0.125109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.18335 | 0.257416 | 0.128708 | − | 0.991683i | \(-0.458917\pi\) | ||||
0.128708 | + | 0.991683i | \(0.458917\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.81665 | −0.324289 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.39445 | 0.306247 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.0000 | 0.866763 | 0.433381 | − | 0.901211i | \(-0.357320\pi\) | ||||
0.433381 | + | 0.901211i | \(0.357320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.2111 | 0.832784 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.2389 | 1.20070 | 0.600348 | − | 0.799739i | \(-0.295029\pi\) | ||||
0.600348 | + | 0.799739i | \(0.295029\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.18335 | 0.171500 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6056 | 0.923638 | 0.461819 | − | 0.886974i | \(-0.347197\pi\) | ||||
0.461819 | + | 0.886974i | \(0.347197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.6333 | −0.433742 | −0.216871 | − | 0.976200i | \(-0.569585\pi\) | ||||
−0.216871 | + | 0.976200i | \(0.569585\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.2111 | 0.415140 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6056 | 0.998709 | 0.499354 | − | 0.866398i | \(-0.333571\pi\) | ||||
0.499354 | + | 0.866398i | \(0.333571\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −60.8444 | −2.46150 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.8444 | 1.16501 | 0.582507 | − | 0.812825i | \(-0.302072\pi\) | ||||
0.582507 | + | 0.812825i | \(0.302072\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.4500 | −1.54794 | −0.773969 | − | 0.633224i | \(-0.781731\pi\) | ||||
−0.773969 | + | 0.633224i | \(0.781731\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.6333 | −1.43222 | −0.716112 | − | 0.697986i | \(-0.754080\pi\) | ||||
−0.716112 | + | 0.697986i | \(0.754080\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −36.0000 | −1.44231 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.21110 | 0.128035 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.02776 | −0.239961 | −0.119981 | − | 0.992776i | \(-0.538283\pi\) | ||||
−0.119981 | + | 0.992776i | \(0.538283\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.2111 | −0.762369 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.39445 | 0.0552501 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.0000 | 0.947943 | 0.473972 | − | 0.880540i | \(-0.342820\pi\) | ||||
0.473972 | + | 0.880540i | \(0.342820\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.0278 | −0.513765 | −0.256882 | − | 0.966443i | \(-0.582695\pi\) | ||||
−0.256882 | + | 0.966443i | \(0.582695\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.7889 | −0.935238 | −0.467619 | − | 0.883930i | \(-0.654888\pi\) | ||||
−0.467619 | + | 0.883930i | \(0.654888\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.42221 | −0.252094 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.2389 | −0.909407 | −0.454703 | − | 0.890643i | \(-0.650255\pi\) | ||||
−0.454703 | + | 0.890643i | \(0.650255\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | 0.234439 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.3944 | −0.521774 | −0.260887 | − | 0.965369i | \(-0.584015\pi\) | ||||
−0.260887 | + | 0.965369i | \(0.584015\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.8444 | 1.35529 | 0.677645 | − | 0.735389i | \(-0.263001\pi\) | ||||
0.677645 | + | 0.735389i | \(0.263001\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.39445 | 0.364301 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.18335 | 0.161980 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.3944 | 0.748714 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.0278 | 0.964749 | 0.482375 | − | 0.875965i | \(-0.339774\pi\) | ||||
0.482375 | + | 0.875965i | \(0.339774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.6333 | 0.831436 | 0.415718 | − | 0.909494i | \(-0.363530\pi\) | ||||
0.415718 | + | 0.909494i | \(0.363530\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.8444 | −0.799935 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.00000 | −0.344375 | −0.172188 | − | 0.985064i | \(-0.555084\pi\) | ||||
−0.172188 | + | 0.985064i | \(0.555084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.8167 | −0.642531 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.6056 | −0.404039 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.60555 | −0.365412 | −0.182706 | − | 0.983168i | \(-0.558486\pi\) | ||||
−0.182706 | + | 0.983168i | \(0.558486\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00000 | 0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.39445 | −0.280085 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.5778 | 0.437287 | 0.218644 | − | 0.975805i | \(-0.429837\pi\) | ||||
0.218644 | + | 0.975805i | \(0.429837\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.21110 | 0.271972 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.2666 | −1.17590 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8444 | 0.857940 | 0.428970 | − | 0.903319i | \(-0.358877\pi\) | ||||
0.428970 | + | 0.903319i | \(0.358877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.8167 | −0.629789 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30.4222 | −1.13773 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.2666 | −1.38981 | −0.694905 | − | 0.719101i | \(-0.744554\pi\) | ||||
−0.694905 | + | 0.719101i | \(0.744554\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4222 | 0.388143 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.39445 | 0.0517885 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.6333 | 1.32157 | 0.660783 | − | 0.750577i | \(-0.270224\pi\) | ||||
0.660783 | + | 0.750577i | \(0.270224\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.972244 | 0.0359597 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.0000 | −1.18195 | −0.590973 | − | 0.806691i | \(-0.701256\pi\) | ||||
−0.590973 | + | 0.806691i | \(0.701256\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.63331 | 0.133835 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.02776 | 0.221735 | 0.110867 | − | 0.993835i | \(-0.464637\pi\) | ||||
0.110867 | + | 0.993835i | \(0.464637\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.57779 | 0.204629 | 0.102315 | − | 0.994752i | \(-0.467375\pi\) | ||||
0.102315 | + | 0.994752i | \(0.467375\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.0278 | 0.843672 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.0278 | −1.09573 | −0.547864 | − | 0.836567i | \(-0.684559\pi\) | ||||
−0.547864 | + | 0.836567i | \(0.684559\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.4222 | 0.524878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.7889 | −0.610203 | −0.305101 | − | 0.952320i | \(-0.598690\pi\) | ||||
−0.305101 | + | 0.952320i | \(0.598690\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.4500 | −0.415061 | −0.207530 | − | 0.978229i | \(-0.566543\pi\) | ||||
−0.207530 | + | 0.978229i | \(0.566543\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.2389 | −0.660291 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.21110 | 0.332594 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.0000 | 1.47850 | 0.739249 | − | 0.673432i | \(-0.235181\pi\) | ||||
0.739249 | + | 0.673432i | \(0.235181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.81665 | −0.173243 | −0.0866215 | − | 0.996241i | \(-0.527607\pi\) | ||||
−0.0866215 | + | 0.996241i | \(0.527607\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.60555 | −0.201357 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.6056 | −0.594956 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.0555 | −1.21860 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.8167 | 0.635904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.0278 | 1.39119 | 0.695595 | − | 0.718434i | \(-0.255141\pi\) | ||||
0.695595 | + | 0.718434i | \(0.255141\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.6333 | −1.40920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.8167 | −0.987798 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.6611 | 1.47571 | 0.737855 | − | 0.674959i | \(-0.235839\pi\) | ||||
0.737855 | + | 0.674959i | \(0.235839\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.7889 | −0.523194 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 58.0555 | 2.04873 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.81665 | −0.275501 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.3944 | −1.52567 | −0.762834 | − | 0.646595i | \(-0.776193\pi\) | ||||
−0.762834 | + | 0.646595i | \(0.776193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5778 | −0.476781 | −0.238390 | − | 0.971169i | \(-0.576620\pi\) | ||||
−0.238390 | + | 0.971169i | \(0.576620\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | −0.0700569 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.18335 | 0.0763856 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.8167 | −0.621050 | −0.310525 | − | 0.950565i | \(-0.600505\pi\) | ||||
−0.310525 | + | 0.950565i | \(0.600505\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.2111 | −1.67646 | −0.838232 | − | 0.545314i | \(-0.816411\pi\) | ||||
−0.838232 | + | 0.545314i | \(0.816411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.7889 | 0.444177 | 0.222088 | − | 0.975027i | \(-0.428713\pi\) | ||||
0.222088 | + | 0.975027i | \(0.428713\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.338936 | 0.0117434 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.00000 | 0.103819 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.2111 | −1.14657 | −0.573287 | − | 0.819354i | \(-0.694332\pi\) | ||||
−0.573287 | + | 0.819354i | \(0.694332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0555 | −0.932949 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.6333 | 1.05382 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.6056 | −0.914178 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.2111 | −1.00017 | −0.500085 | − | 0.865977i | \(-0.666698\pi\) | ||||
−0.500085 | + | 0.865977i | \(0.666698\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.23886 | −0.178956 | −0.0894780 | − | 0.995989i | \(-0.528520\pi\) | ||||
−0.0894780 | + | 0.995989i | \(0.528520\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.0278 | 1.02453 | 0.512267 | − | 0.858826i | \(-0.328806\pi\) | ||||
0.512267 | + | 0.858826i | \(0.328806\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.2111 | −1.02840 | −0.514199 | − | 0.857671i | \(-0.671911\pi\) | ||||
−0.514199 | + | 0.857671i | \(0.671911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.8167 | −0.367777 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −53.4500 | −1.81317 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.21110 | −0.176571 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.60555 | −0.0880837 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.6611 | −0.765210 | −0.382605 | − | 0.923912i | \(-0.624973\pi\) | ||||
−0.382605 | + | 0.923912i | \(0.624973\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.3944 | 0.855561 | 0.427780 | − | 0.903883i | \(-0.359296\pi\) | ||||
0.427780 | + | 0.903883i | \(0.359296\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.8167 | −0.532273 | −0.266136 | − | 0.963935i | \(-0.585747\pi\) | ||||
−0.266136 | + | 0.963935i | \(0.585747\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.6333 | 1.02857 | 0.514283 | − | 0.857621i | \(-0.328058\pi\) | ||||
0.514283 | + | 0.857621i | \(0.328058\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.0555 | 1.67881 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.2111 | −1.11137 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.2111 | −0.709009 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.81665 | −0.260700 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.57779 | −0.0858788 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.00000 | 0.232688 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.57779 | −0.0523898 | −0.0261949 | − | 0.999657i | \(-0.508339\pi\) | ||||
−0.0261949 | + | 0.999657i | \(0.508339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.02776 | 0.166577 | 0.0832885 | − | 0.996525i | \(-0.473458\pi\) | ||||
0.0832885 | + | 0.996525i | \(0.473458\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.8167 | 0.457265 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.6333 | −0.516257 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.4222 | 0.871588 | 0.435794 | − | 0.900046i | \(-0.356468\pi\) | ||||
0.435794 | + | 0.900046i | \(0.356468\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.8444 | 1.60773 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.3944 | −0.636311 | −0.318156 | − | 0.948039i | \(-0.603063\pi\) | ||||
−0.318156 | + | 0.948039i | \(0.603063\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.761141 | 0.0249454 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.39445 | −0.241824 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.2111 | 1.34631 | 0.673154 | − | 0.739502i | \(-0.264939\pi\) | ||||
0.673154 | + | 0.739502i | \(0.264939\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.422205 | −0.0137635 | −0.00688175 | − | 0.999976i | \(-0.502191\pi\) | ||||
−0.00688175 | + | 0.999976i | \(0.502191\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.8167 | 0.449932 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.0000 | 1.26733 | 0.633665 | − | 0.773608i | \(-0.281550\pi\) | ||||
0.633665 | + | 0.773608i | \(0.281550\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −83.2666 | −2.70295 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.8444 | 0.999148 | 0.499574 | − | 0.866271i | \(-0.333490\pi\) | ||||
0.499574 | + | 0.866271i | \(0.333490\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.4222 | 0.401973 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.8167 | 1.41491 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.422205 | 0.0136195 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.183346 | 0.00590212 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0000 | 1.60789 | 0.803946 | − | 0.594703i | \(-0.202730\pi\) | ||||
0.803946 | + | 0.594703i | \(0.202730\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | −0.577647 | −0.288824 | − | 0.957382i | \(-0.593264\pi\) | ||||
−0.288824 | + | 0.957382i | \(0.593264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.4222 | −0.334121 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.2111 | 0.486646 | 0.243323 | − | 0.969945i | \(-0.421762\pi\) | ||||
0.243323 | + | 0.969945i | \(0.421762\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63.6333 | 2.03373 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.6333 | 1.35979 | 0.679896 | − | 0.733309i | \(-0.262025\pi\) | ||||
0.679896 | + | 0.733309i | \(0.262025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.8167 | −0.726999 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.81665 | −0.0577662 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.1833 | −0.927040 | −0.463520 | − | 0.886087i | \(-0.653414\pi\) | ||||
−0.463520 | + | 0.886087i | \(0.653414\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.21110 | −0.0383945 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.8722 | 1.26276 | 0.631382 | − | 0.775472i | \(-0.282488\pi\) | ||||
0.631382 | + | 0.775472i | \(0.282488\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8640.2.a.df.1.1 | 2 | ||
3.2 | odd | 2 | 8640.2.a.cr.1.1 | 2 | |||
4.3 | odd | 2 | 8640.2.a.cy.1.2 | 2 | |||
8.3 | odd | 2 | 2160.2.a.y.1.2 | 2 | |||
8.5 | even | 2 | 135.2.a.d.1.2 | yes | 2 | ||
12.11 | even | 2 | 8640.2.a.ck.1.2 | 2 | |||
24.5 | odd | 2 | 135.2.a.c.1.1 | ✓ | 2 | ||
24.11 | even | 2 | 2160.2.a.ba.1.2 | 2 | |||
40.13 | odd | 4 | 675.2.b.h.649.1 | 4 | |||
40.29 | even | 2 | 675.2.a.k.1.1 | 2 | |||
40.37 | odd | 4 | 675.2.b.h.649.4 | 4 | |||
56.13 | odd | 2 | 6615.2.a.v.1.2 | 2 | |||
72.5 | odd | 6 | 405.2.e.k.136.2 | 4 | |||
72.13 | even | 6 | 405.2.e.j.136.1 | 4 | |||
72.29 | odd | 6 | 405.2.e.k.271.2 | 4 | |||
72.61 | even | 6 | 405.2.e.j.271.1 | 4 | |||
120.29 | odd | 2 | 675.2.a.p.1.2 | 2 | |||
120.53 | even | 4 | 675.2.b.i.649.4 | 4 | |||
120.77 | even | 4 | 675.2.b.i.649.1 | 4 | |||
168.125 | even | 2 | 6615.2.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.a.c.1.1 | ✓ | 2 | 24.5 | odd | 2 | ||
135.2.a.d.1.2 | yes | 2 | 8.5 | even | 2 | ||
405.2.e.j.136.1 | 4 | 72.13 | even | 6 | |||
405.2.e.j.271.1 | 4 | 72.61 | even | 6 | |||
405.2.e.k.136.2 | 4 | 72.5 | odd | 6 | |||
405.2.e.k.271.2 | 4 | 72.29 | odd | 6 | |||
675.2.a.k.1.1 | 2 | 40.29 | even | 2 | |||
675.2.a.p.1.2 | 2 | 120.29 | odd | 2 | |||
675.2.b.h.649.1 | 4 | 40.13 | odd | 4 | |||
675.2.b.h.649.4 | 4 | 40.37 | odd | 4 | |||
675.2.b.i.649.1 | 4 | 120.77 | even | 4 | |||
675.2.b.i.649.4 | 4 | 120.53 | even | 4 | |||
2160.2.a.y.1.2 | 2 | 8.3 | odd | 2 | |||
2160.2.a.ba.1.2 | 2 | 24.11 | even | 2 | |||
6615.2.a.p.1.1 | 2 | 168.125 | even | 2 | |||
6615.2.a.v.1.2 | 2 | 56.13 | odd | 2 | |||
8640.2.a.ck.1.2 | 2 | 12.11 | even | 2 | |||
8640.2.a.cr.1.1 | 2 | 3.2 | odd | 2 | |||
8640.2.a.cy.1.2 | 2 | 4.3 | odd | 2 | |||
8640.2.a.df.1.1 | 2 | 1.1 | even | 1 | trivial |